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Simplifying 9x4 + -12x3 + x2 = 0 Reorder the terms: x2 + -12x3 + 9x4 = 0 Solving x2 + -12x3 + 9x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(1 + -12x + 9x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(1 + -12x + 9x2)' equal to zero and attempt to solve: Simplifying 1 + -12x + 9x2 = 0 Solving 1 + -12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + -1.333333333x + -0.1111111111 + x2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + -1.333333333x + x2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + -1.333333333x + x2 = 0 + -0.1111111111 -1.333333333x + x2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 -1.333333333x + x2 = -0.1111111111 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = -0.1111111111 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -0.1111111111 + 0.4444444442 Combine like terms: -0.1111111111 + 0.4444444442 = 0.3333333331 0.4444444442 + -1.333333333x + x2 = 0.3333333331 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 0.3333333331 Calculate the square root of the right side: 0.577350269 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 0.577350269 and -0.577350269.Subproblem 1
x + -0.6666666665 = 0.577350269 Simplifying x + -0.6666666665 = 0.577350269 Reorder the terms: -0.6666666665 + x = 0.577350269 Solving -0.6666666665 + x = 0.577350269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 0.577350269 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 0.577350269 + 0.6666666665 x = 0.577350269 + 0.6666666665 Combine like terms: 0.577350269 + 0.6666666665 = 1.2440169355 x = 1.2440169355 Simplifying x = 1.2440169355Subproblem 2
x + -0.6666666665 = -0.577350269 Simplifying x + -0.6666666665 = -0.577350269 Reorder the terms: -0.6666666665 + x = -0.577350269 Solving -0.6666666665 + x = -0.577350269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -0.577350269 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -0.577350269 + 0.6666666665 x = -0.577350269 + 0.6666666665 Combine like terms: -0.577350269 + 0.6666666665 = 0.0893163975 x = 0.0893163975 Simplifying x = 0.0893163975Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2440169355, 0.0893163975}Solution
x = {0, 1.2440169355, 0.0893163975}
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